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In polynomial long division, what is the first step when dividing 4x^3 + 2x^2 -

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Question: In polynomial long division, what is the first step when dividing 4x^3 + 2x^2 - x by 2x + 1?

Options:

  1. Multiply the divisor by the leading term of the dividend.
  2. Subtract the product from the dividend.
  3. Identify the degree of both polynomials.
  4. Write the remainder.

Correct Answer: Multiply the divisor by the leading term of the dividend.

Solution: 

The first step in polynomial long division is to multiply the divisor by the leading term of the dividend.

In polynomial long division, what is the first step when dividing 4x^3 + 2x^2 -

Practice Questions

Q1
In polynomial long division, what is the first step when dividing 4x^3 + 2x^2 - x by 2x + 1?
  1. Multiply the divisor by the leading term of the dividend.
  2. Subtract the product from the dividend.
  3. Identify the degree of both polynomials.
  4. Write the remainder.

Questions & Step-by-Step Solutions

In polynomial long division, what is the first step when dividing 4x^3 + 2x^2 - x by 2x + 1?
  • Step 1: Identify the leading term of the dividend, which is 4x^3.
  • Step 2: Identify the leading term of the divisor, which is 2x.
  • Step 3: Divide the leading term of the dividend (4x^3) by the leading term of the divisor (2x) to find the first term of the quotient.
  • Step 4: Multiply the entire divisor (2x + 1) by the result from Step 3 to prepare for subtraction.
  • Polynomial Long Division – The process of dividing a polynomial by another polynomial, similar to numerical long division.
  • Leading Term Identification – Identifying the leading term of both the dividend and the divisor to determine the first step in the division process.
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